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Sliding-Mode Filter Design for Linear Systems With Unmeasured States

Sliding-Mode Filter Design for Linear Systems With Unmeasured States,10.1109/TIE.2010.2081959,IEEE Transactions on Industrial Electronics,Michael V. B

Sliding-Mode Filter Design for Linear Systems With Unmeasured States  
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This paper addresses the mean-square and mean- module filtering problems for a linear system with Gaussian white noises. The obtained solutions contain a sliding-mode term, signum of the innovation process. It is shown that the designed sliding-mode mean-square filter generates the mean-square esti- mate, which has the same minimum estimation-error variance as the best estimate given by the classical Kalman-Bucy filter, al- though the gain matrices of both filters are different. The designed sliding-mode mean-module filter generates the mean-module es- timate, which yields a better value of the mean-module criterion in comparison with the mean-square Kalman-Bucy filter. The theoretical result is complemented with an illustrative example verifying the performance of the designed filters. It is demon- strated that the estimates produced by the designed sliding-mode mean-square filter and the Kalman-Bucy filter yield the same estimation-error variance, and there is an advantage in favor of the designed sliding-mode mean-module filter.
Journal: IEEE Transactions on Industrial Electronics - IEEE TRANS IND ELECTRON , vol. 58, no. 8, pp. 3616-3622, 2011
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